1. Teaching Statistical Concepts with Simulated Data Andrej Blejec National Institute of Biology and University of Ljubljana Ljubljana, Slovenia andrej.blejec@nib.si

2. Kinds of data real life data invented data simulated data Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

3. Real life data interesting for students need subject matter knowledge to interpret statistical results oversimplified problems complex problems unclear relevance of statistical results Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

4. Invented data a collection of data, no story useful mostly for calculation drill no possible interpretation of results uninteresting for students Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

5. Simulated data sampled from known distribution composed according to prespecified model e.g. Y = a + b * X + , with known distribution of X and  known statistical properties e.g. mean, variance, regression coefficient analysis results can be compared to true values Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

6. Goals of teaching statistics interest for statistics understanding of statistical methods skills in use of statistics experiences in analyzing data other ( insert your own :) ___________ Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

8. Sun Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011 Absorption spectrum

9. Sun Hydrogen Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

10. Sun Hydrogen Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

22. Least squares estimate of the mean

23. Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011 Mean squared deviations

24. Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011 Mean squared deviations

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37. Mean squared deviations

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47. Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011 Mean squared deviations

48. True mean value μ LS estimate Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011 Mean squared deviations

49. Maximum likelihood estimation of the mean

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82. True mean value μ ML estimate Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

88. Maximum likelihood estimate of standard deviation Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

89. Log likelihood p ( x | sd ) Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

90. Log likelihood p ( x | sd ) Log likelihood p ( x | sd ) Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

91. Log likelihood p ( x | sd ) Log likelihood p ( x | sd ) Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

92. Log likelihood p ( x | sd ) Log likelihood p ( x | sd ) Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

93. Log likelihood p ( x | sd ) Log likelihood p ( x | sd ) Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

94. Log likelihood p ( x | sd ) Log likelihood p ( x | sd ) Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

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118. Log likelihood p ( x | sd ) Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

119. Log likelihood p ( x | sd ) ML estimate True standard deviation σ Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

120. Hypothesis testing: significance Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

121. Hypothesis testing: significance or rather a surprise ? Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

132. Confidence intervals Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

133. Weldon, K.L. Statistics: A Conceptual Approach.. Prentice-Hall. New York. 1986 Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

151. Bad sampling implies bias Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

152. Bias due to “leave max out” Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

153. Confidence intervals for variance Biased and unbiased estimators

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157. unbiased Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

163. Confidence intervals for variance: what if assumptions are not met? Case of asymetric parent population

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172. Confidence band in linear regression Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

176. Coefficient of determination

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185. Final remarks Graphically supported simulations can ‑ to some extent ‑ replace the proofs, usually not understandable to non-mathematics majors. Maybe they are the answer to some questions: "If an audience is not convinced by proof, why do proof? (Moore, 1996) “Do [students] need to know the theory or do they need to understand the concept?” (J Brown and I David, ICOTS8, 2010) Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

186. Simulated data have to be combined with real life data and projects Simulated data can serve as pure and simple data on which we can train our perception for statistical results and learn what patterns and properties in data can be revealed by applied method After such preparation students will be able to interpret the real life and subject matter data in all their complexity Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011